An approximation method for a single server queue with cyclically indexed arrival and service rates

Abstract

In this paper we develop an approximation scheme for a single server Markovian queue with cyclic arrival and/or service patterns. The arrival and service patterns change cyclically according to a job (or customer) sequence number. The model has found application in production planning for multiple items on constrained resources using cyclic schedules. It has also been applied to a computer simulation sensitivity analysis technique called Frequency Domain Methodology. The approximation scheme provides results to any desired degree of accuracy. Performance guidelines for the approximation are established analytically using stochastic ordering. In addition, performance results are numerically evaluated for the model with cyclic arrival patterns and independent and identically distributed exponential service patterns using a nonlinear optimization model.